Firemen use a high-pressure hose to shoot a stream of water at a burning building. The water has a speed of 25.0 m/s as it leaves the end of the hose and then exhibits projectile motion. The firemen adjust the angle of elevation ? of the hose until the water takes 3.00 s to reach a building 45.0 m away. Ignore air resistance; assume that the end of the hose is at ground level. (a) Find ?. (b) Find the speed and acceleration of the water at the highest point in its trajectory. (c) How high above the ground does the water strike the building, and how fast is it moving just before it hits the building?
Solution 22 E Step 1 : In this question, we need to find the Angle of incident Find the speed and acceleration of water at the highest point in trajectory How high above the ground the water strikes the building and how fast is it moving just before it hits the building Step 2 : Let us consider the data given Horizontal distance of the building x 45 m Initial velocity of the water v = 25 m/s i Time taken to reach the building t = 3.0 s Step 3 : Let us find the angle at which the water hits the building It is obtained using x = x0+ v ti The x - component is given by x0= v cis Substituting this in above equation we get x = v ios + v i Substituting the values we get 45 m = 25 m/s cos × 3.0 s Resolving this to find the angle we get 45 m cos = 25 m/s ×3 45 m cos = 75 m/s = cos (0.6) = 53.13 0 Hence the angle at which the the water hits the hose is 53.13 0 Step 4 : We shall now find the maximum speed and acceleration of the water when it reaches the height of the building This maximum velocity is given by vox = v i cos 53.13 vox = 25 m/s × cos 53.13 vox = 15 m/s Hence the maximum speed of water with which it hits the building is 15 m/s